Launchings

Disturbing Trends in the CBMS Data

The CBMS Statistical Abstract of Undergraduate Programs [1]
is a source of information that I have mined for many of these columns. For
this month, I would like to draw attention to a trend that I find very disturbing:
While college calculus enrollments and the total number of mathematics majors
have been roughly constant over the period 1990–2005, there has been
a steady decline in enrollments at both small colleges and comprehensive universities.
All of the growth has occurred at the major research universities. This shift
in the site where mathematics is studied has implications that I shall address
in four sections:

In the graphs that follow, the three types of institutions are labeled as
"research universities," "comprehensive universities,"
or "undergraduate colleges." The actual determination of institution
type in the CBMS data is by the highest degree in mathematics that is offered
at the institution: PhD, MA, or BA. The graph shown below gives the total
number of bachelor's degrees in Mathematics, including dual degrees of Mathematics
with another specialty, by type of institution. It does not include degrees
in Mathematics Education, Statistics, or Operations Research.

While some universities have added graduate programs over the
past fifteen years, the overall numbers are stable enough to be able to draw
conclusions, as the graph below of "BA/BS in
Math per Institution" illustrates.

Mathematics and Engineering

Among the striking features of this graph is that the three types of institutions
exhibit little similarity in their patterns of growth and decline. The NSF
VIGRE grants have been one factor affecting the growth in majors at research
universities over the period 2000–05. I suspect that they have had a
measurable impact, but the pattern of math majors at PhD-granting universities
is also highly correlated with that of engineering majors (engineering data
from [2]). We only have four data points: 1990 through
2005, but the correlation coefficient is a substantial 0.909. In particular,
the pattern of decline over the decade 1990–2000 followed by a sharp
increase from 2000 to 2005 is common to both.

The correlation is only with Engineering and not more broadly
with STEM majors. The Biological Sciences grew by almost 50% from 1990 to
1995, stagnated for five years, and then grew by another 16% from 2000 to
2005. The Physical Sciences grew by a more modest but still substantial 20%
from 1990 to 1995, lost about half of that growth from 1995 to 2000, and have
since returned to just above the 1995 number. Computer Science and Information
Technology was stagnant from 1990 to 1995, almost doubled from 1995 to 2000,
and has seen very modest growth since then [2].

Small colleges have seen a small net growth over the 15 years 1990–2005,
but what is most noticeable is the sharp drop from 2000 to 2005. Comprehensive
universities have experienced a marked decrease in majors, dropping by over
a third since 1990. The recent decline in majors at small colleges and the
erosion of majors at comprehensive universities is disturbing because it raises
questions about the long-term viability of these programs.

Women in Mathematics

The shift of majors from small colleges and comprehensive universities to
research universities is also disturbing for another reason. Research universities
have traditionally done worse than small colleges and comprehensive universities
at attracting women to the mathematics major. In 2005, women made up 43% of
the math majors at colleges where the highest available degree in mathematics
was either a BA or an MA. The figure was below 36% at PhD granting universities.
After reaching a high of 44% of all math majors in 1995, the percentage of
women has been declining, and is now just under 40%.

The decline in the percentage of women among math majors has been masked
by the fact that women make up 60% of majors in mathematics education and
48% of those majoring in statistics. Combining mathematics, mathematics education,
and statistics, women constitute almost 44% of these majors. Nevertheless,
the decline in math majors as such should be of concern because it will impact
both the recruitment of women into graduate programs and the presence of women
in the mathematical workforce.

As the graph below illustrates, the problems are not unique to research universities.
The percentage of women among math majors has been generally decreasing across
all types of institutions. In fact, research universities are the only types
of institutions that today are ahead of where they were in 1990. But as a
whole, they have trailed well below small colleges and comprehensive universities
in their ability to attract women to mathematics, and their increasing dominance
as the source of math majors only promises to accelerate the decline.

The Danger for Small Colleges

The implications of the decline over the past five years in
the number of majors coming from BA institutions is clearer when we look at
the average number of majors per college.

When small colleges lose mathematics enrollments and majors,
it is easy to tip into a situation where standard upper division courses can
no longer be offered. This may be behind the CBMS data revealing a substantial
number of 4-year colleges that no longer offer modern algebra and/or real
analysis on a regular basis (at least once every two years). See my column
from February, 2007, What
has happened to Modern Algebra and Real Analysis?. With an average
of only 5.6 majors per year, a college does not have to be very far below
average before it becomes difficult to offer advanced courses on a regular
basis.

The peak of 6.8 in 2000 is too large to be attributable to random
fluctuation. My best guess is that this was driven by the explosion of growth
in computer science during the period 1995–2000. At many small colleges,
the computer science program sits within the mathematics department or is
closely allied with it so that computer science majors find it easy to add
or switch to a math major. And while, nationally, computer science majors
have grown since 2000, it appears that this growth has been entirely at the
large universities. Computer science enrollments at Macalester dropped sharply
after 2000, and my evidence from colleagues at other small colleges is that
we have all suffered a sharp decrease in computer science enrollments.

Calculus Enrollments

While it is good news that majors are up substantially at the research universities,
I also have some concern here because calculus classes at large universities
are large and getting larger, and increasingly they are taught by adjunct
faculty. (See my column from October, 2007, Who
Teaches Our Calculus Classes?) As the CBMS data make clear, the only
reason that enrollments in Calculus II and III are holding steady is because
they are increasing in our large universities. Everywhere else, these enrollments
are in decline. These graphs include enrollments in two-year colleges.

The pattern of calculus enrollments at PhD-granting universities
over the period 1990–2000 mirrors the number of graduates in mathematics
(as well as the number of graduates in engineering), but occurs three to four
years earlier as one would expect. The increase in calculus enrollments from
1995 to 2005 is actually very close to the increase in total college enrollments
over that period (22.6% increase [2]), and the growth
trails the national increase in enrollment (25.6%) if we look at the period
1990–2005.

The steady decline in calculus enrollments at comprehensive
universities, small colleges, and two-year colleges occurs in the face of
a substantial increase in total enrollment and is thus all the more remarkable
and discouraging.

Conclusion

At our large research universities, engineering is the main
driver for both calculus enrollments and the creation of a pool of potential
math majors. Away from these universities, both enrollments in Calculus II
and higher and the number of math majors are in a slow but steady decline.
This is particularly surprising and discouraging because the number of first-year
students who arrive with college credit for a calculus course taken while
in high school has grown from about 60,000 in 1990 to almost 200,000 in 2005.
Calculus II fall enrollments should not be dropping anywhere.

Even where we see growth, it is below the rate of growth in
total enrollment.

It should not be this way. Mathematics is a core discipline
that should be building cooperative programs with many different disciplines.
It should be capable of capitalizing on growth in any of the sciences, most
especially the biological sciences. The data show that there is still much
to do.

David Bressoud
is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul,
Minnesota, and president-elect of the MAA. You can reach him at bressoud@macalester.edu.
This column does not reflect an official position of the MAA.